19 research outputs found
Interlayer antisynchronization in degree-biased duplex networks
With synchronization being one of nature's most ubiquitous collective
behaviors, the field of network synchronization has experienced tremendous
growth, leading to significant theoretical developments. However, most of these
previous studies consider uniform connection weights and undirected networks
with positive coupling. In the present article, we incorporate the asymmetry in
a two-layer multiplex network by assigning the ratio of the adjacent nodes'
degrees as the weights to the intralayer edges. Despite the presence of
degree-biased weighting mechanism and attractive-repulsive coupling strengths,
we are able to find the necessary conditions for intralayer synchronization and
interlayer antisynchronization and test whether these two macroscopic states
can withstand demultiplexing in a network. During the occurrence of these two
states, we analytically calculate the oscillator's amplitude. In addition to
deriving the local stability conditions for interlayer antisynchronization via
the master stability function approach, we also construct a suitable Lyapunov
function to determine a sufficient condition for global stability. We provide
numerical evidence to show the necessity of negative interlayer coupling
strength for the occurrence of antisynchronization, and such repulsive
interlayer coupling coefficients can not destroy intralayer synchronization.Comment: 16 pages, 5 figures (Accepted for publication in the journal Physical
Review E
Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions
The persistence of biodiversity of species is a challenging proposition in
ecological communities in the face of Darwinian selection. The present article
investigates beyond the pairwise competitive interactions and provides a novel
perspective for understanding the influence of higher-order interactions on the
evolution of social phenotypes. Our simple model yields a prosperous outlook to
demonstrate the impact of perturbations on intransitive competitive
higher-order interactions. Using a mathematical technique, we show how alone
the perturbed interaction network can quickly determine the coexistence
equilibrium of competing species instead of solving a large system of ordinary
differential equations. It is possible to split the system into multiple
feasible cluster states depending on the number of perturbations. Our analysis
also reveals the ratio between the unperturbed and perturbed species is
inversely proportional to the amount of employed perturbation. Our results
suggest that nonlinear dynamical systems and interaction topologies can be
interplayed to comprehend species' coexistence under adverse conditions.
Particularly our findings signify that less competition between two species
increases their abundance and outperforms others.Comment: 17 pages, 10 figure
Swarmalators under competitive time-varying phase interactions
Swarmalators are entities with the simultaneous presence of swarming and
synchronization that reveal emergent collective behavior due to the fascinating
bidirectional interplay between phase and spatial dynamics. Although different
coupling topologies have already been considered, here we introduce
time-varying competitive phase interaction among swarmalators where the
underlying connectivity for attractive and repulsive coupling varies depending
on the vision (sensing) radius. Apart from investigating some fundamental
properties like conservation of center of position and collision avoidance, we
also scrutinize the cases of extreme limits of vision radius. The concurrence
of attractive-repulsive competitive phase coupling allows the exploration of
diverse asymptotic states, like static , and mixed phase wave states, and
we explore the feasible routes of those states through a detailed numerical
analysis. In sole presence of attractive local coupling, we reveal the
occurrence of static cluster synchronization where the number of clusters
depends crucially on the initial distribution of positions and phases of each
swarmalator. In addition, we analytically calculate the sufficient condition
for the emergence of the static synchronization state. We further report the
appearance of the static ring phase wave state and evaluate its radius
theoretically. Finally, we validate our findings using Stuart-Landau
oscillators to describe the phase dynamics of swarmalators subject to
attractive local coupling.Comment: 21 pages, 12 figures; accepted for publication in New Journal of
Physic
Consensus Formation Among Mobile Agents in Networks of Heterogeneous Interaction Venues
Exploring the collective behavior of interacting entities is of great
interest and importance. Rather than focusing on static and uniform
connections, we examine the co-evolution of diverse mobile agents experiencing
varying interactions across both space and time. Analogous to the social
dynamics of intrinsically diverse individuals who navigate between and interact
within various physical or digital locations, agents in our model traverse a
complex network of heterogeneous environments and engage with everyone they
encounter. The precise nature of agents internal dynamics and the various
interactions that nodes induce are left unspecified and can be tailored to suit
the requirements of individual applications. We derive effective dynamical
equations for agent states which are instrumental in investigating thresholds
of consensus, devising effective attack strategies to hinder coherence, and
designing optimal network structures with inherent node variations in mind. We
demonstrate that agent cohesion can be promoted by increasing agent density,
introducing network heterogeneity, and intelligently designing the network
structure, aligning node degrees with the corresponding interaction strengths
they facilitate. Our findings are applied to two distinct scenarios: the
synchronization of brain activities between interacting individuals, as
observed in recent collective MRI scans, and the emergence of consensus in a
cusp catastrophe model of opinion dynamics.Comment: 18 pages, 10 figure
Extreme rotational events in a forced-damped nonlinear pendulum
Since Galileo's time, the pendulum has evolved into one of the most exciting
physical objects in mathematical modeling due to its vast range of applications
for studying various oscillatory dynamics, including bifurcations and chaos,
under various interests. This well-deserved focus aids in comprehending various
oscillatory physical phenomena that can be reduced to the equations of the
pendulum. The present article focuses on the rotational dynamics of the
two-dimensional forced damped pendulum under the influence of the ac and dc
torque. Interestingly, we are able to detect a range of the pendulum's length
for which the angular velocity exhibits a few intermittent extreme rotational
events that deviate significantly from a certain well-defined threshold. The
statistics of the return intervals between these extreme rotational events are
supported by our data to be spread exponentially. The numerical results show a
sudden increase in the size of the chaotic attractor due to interior crisis
which is the source of instability that is responsible for triggering large
amplitude events in our system. We also notice the occurrence of phase slips
with the appearance of extreme rotational events when phase difference between
the instantaneous phase of the system and the externally applied ac torque is
observed.Comment: 10 pages, 7 figures, Comments are welcom
Hidden attractors: A new chaotic system without equilibria
Localization of hidden attractors is one of the most challenging tasks in the nonlinear dynamics due to deficiency of properly justified analytical and numerical procedures. But understanding about the emergence of such unexpected occurrence of hidden attractors is desirable, because that can help to diminish the unexpected switch from one attractor to another undesired behavior. We propose a novel autonomous three-dimensional system exhibiting hidden attractor. These attractors can not be tracked using perpetual points. The reason behind this inefficiency is explained using theory of differential equations. Our system consists a slow manifold depicted through the time-series, although the system has no equilibrium points or such multiplicative parameters. We also discuss the behavior of the attractor using time-series analysis, bifurcation theory, Lyapunov spectrum and Kaplan-Yorke dimension. Moreover, the attractor no longer exists for a range of parameter values due to sudden change of strange attractors indicating a possible inverse crisis route to chaos
Synchronization in dynamic network using threshold control approach
Synchronization in time-varying (i.e., dynamic) network has been explored using different types of couplings during the last two decades. In this paper, we consider a dynamic network where the spatial position of each node decides the number of nodes with which it interacts. We analytically derive the density-dependent threshold of coupling strength for synchrony using linear stability analysis and numerically verify the obtained results. We use two paradigmatic chaotic systems, namely the Rössler and Lorenz models to affirm our claims
Perspective on attractive-repulsive interactions in dynamical networks: Progress and future
Emerging collective behavior in complex dynamical networks depends on both coupling function and underlying coupling topology. Through this Perspective, we provide a brief yet profound excerpt of recent research efforts that explore how the synergy of attractive and repulsive interactions influence the destiny of ensembles of interacting dynamical systems. We review the incarnation of collective states ranging from chimera or solitary states to extreme events and oscillation quenching arising as a result of different network arrangements. Though the existing literature demonstrates that many of the crucial developments have been made, nonetheless, we come up with significant routes of further research in this field of study